Mathematics: Pls help meee fellow high schoolers

Pls help meee fellow high schoolers - id9742457, mildredelizam

604341

15.03.2022

x =30°

Step-by-step explanation:

Step 1: To find $\angle \mathrm{KNL}$ .

Given N ∈ KO, where KO is a line.

Sum of the adjacent angles in a straight line is 180°.

$\Rightarrow \angle \mathrm{KNL}+\angle \mathrm{LNM}+\angle \mathrm{MNO}=180^{\circ}$

$\Rightarrow \angle \mathrm{KNL}+45^{\circ}+105^{\circ}=180^{\circ}$

$\Rightarrow \angle \mathrm{KNL}+150^{\circ}=180^{\circ}$

$\Rightarrow \angle \mathrm{KNL}=180^{\circ}-150^{\circ}$

$\Rightarrow \angle \mathrm{KNL}=30^{\circ}$

Step 2: To find $\angle \mathrm{NLK}$ .

Sum of the adjacent angles in a straight line is 180°.

Given $\angle \mathrm{NLM}=90^{\circ}$

$\Rightarrow \angle \mathrm{NLM}+\angle \mathrm{NLK}=180^{\circ}$

$\Rightarrow \angle \mathrm{NLK}=180^{\circ}-90^{\circ}$

$\Rightarrow \angle \mathrm{NLK}=90^{\circ}$

Step 3: To find x.

Sum of the interior angles in a triangle is 180°.

Let us take the triangle NLK.

$\Rightarrow \angle \mathrm{KNL}+\angle \mathrm{NLK}+\angle \mathrm{LKN}=180^{\circ}$

⇒ 30° + 90° + 2x = 180°

⇒ 2x = 180° – 30° – 90°

⇒ 2x = 60°

⇒ x = 30°

Hence, x = 30°.

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